Mode conversion in wave guides



Sept. 11, 1956 s. P. MORGAN, JR

MODE CONVERSION IN WAVE GUIDES Filed May 17, 1951 3 Sheets-Shee. l

ATTORNEV Sept. 1l, 1956 s. P. MORGAN, JR

MODE CONVERSION 1N wAvE GUIDES 3 Sheets-Sheet 2 Filed May 17, 1951 /N/E/VTO/Q s. P MoMA/wx.

77. ,4 ATTO/Q/VEV Sept. 11, 1956 s. P. MORGAN, JR

MODE CONVERSION IN WAVE GUIDES 5 Sheets-Sheet Filed May 17. 1951 ni MODE TRANSDUCER 779/0 SOURCE andasse Referring now to Fig. 1, there is represented diagrammatically at A the electric field configuration characteristic of the TEoi mode in a circular guide, while B and C are applicable similarly to the TEoz and TE o3 modes, respectively. In each case the electric field is symmetrical about the axis and varies in intensity from center to periphery of the guide in known manner. In the TEoi mode the phase is the same from axis to periphery, as indicated by the arrows. In the T E02 mode the phase is the same from the axis out to a cylindrical node of radius p1 equal to 0.54611 where a is the radius of the guide, and the opposite relative phase prevails in the tubular zone extending from that node to the periphery. In the TEos mode there are three such cophasal zones, viz., a central zone extending from the axis to a node of radius p1 equal to 0.377a; an outer cophasal Zone, of the same phase as the first, extending from a node of radius p2 equal to 0.690n to the periphery; and a third cophasal zone, opposite in phase relative to the other two and lying between them.

I have found that if in a wave guide carrying the TEm mode, as in A, dielectric material be placed -in one or the other of the two cophasal zones of B, some of the energy of the operating mode will be converted into the TEoz mode, and further that any tendency to generate noncircular modes can be reduced by disposing the dielectric material symmetrically about the axis of the guide, i. e.,

vin the form of a (solid or hollow) cylinder coaxial with the guide. The maximum generation of the TEoz mode occurs if the dielectric just fills the inner cophasal zone, i. e., the space from the axis of the guide to the first node of the electric field, as illustrated in Fig. 2, or if it just fills the outer cophasal zone, i. e., the space between the first node and the metal shell of the guide, as illustrated in Fig. 3. The two dielectric elements 11, 12, of Figs. 2 and 3, assuming them to be of the same length, are complementary in that the TEoz Waves they generate are equal in amplitude and opposite in phase. This can be readily appreciated on observing that the two (generalized) cylinders together would form a solid dielectric plug filling the guide and that such a plug would generate no modes other than TEoi under the infiuence of a pure TEoi wave.

Similarly, the most efficient disposition of dielectric material for the generation of the 'IEoa mode is in the form of a hollow cylinder or tube 13 just filling the intermediate cophasal zone, as illustrated in Fig. 4, or in the form of a pair of cylinders, 14, 1S, one just filling the inner cophasal zone and the other a tube just filling the outer one, as illustrated in Fig. 5. The dielectric structures in Figs. 4 and 5, respectively, are complementary to each other with respect to the generation of the TEos mode or any other mode.

The same principles are applicable to other guide shapes and modes generally, excepting only unusual cases where the electric field vector of the mode to be generated is perpendicular at every point to the electric field vector of the operating mode. The cophasal zones can be identified readily by superposing the electric field diagrams of the operating mode and the mode to be derived, and marking the boundaries between regions in which the electric vector of the operating mode (or, more generally, the pro- 1 jection thereof) coincides in direction and phase with the electric vector of the other mode, and similar regions in which the relative phases are reversed. Diagram D in Fig. l, for example, illustrates the dominant mode TEio in a guide of rectangular cross section, While at E are illustrated the TEzu mode inthe same guide, the two equal cophasal zones that appear, and the disposition of dielec- Velectric members.

`ifithe guide be of sufficiently small size.

tric material in one of the two cophasal zones for maximum conversion of wave power from the first of these modes to the second. For maximum generation of the TE3o mode the dielectric material may till the central one of the three equal cophasal zones shown at F in Fig. l or it may till both of the adjoining zones which together constitute a cophasal region of the opposite relative phase.

The specific dimensions that have been assigned to the dielectric mode transducers of Figs. 2 to 5 are, as indicated, those that, with a given dielectric material, yield maximum generation of a prescribed secondary mode for a given over-all length of transducer, and it has been pointed out that complementary transducers are equally effective. In various practical applications of the invention, however, other factors than maximum generation are significant or even controlling and they may dictate the choice of one transducer over another or call for modification of the dimensions given. One such factor is ease of fabrication, or mechanical support for the di- The tubular dielectric member in Fig. 3, e.v g., is self-supporting within the guide; the complementary dielectric member in Fig. 2 is not. The latter can be supported by a contiguous dielectric plug (as in Fig. 6); or if the transducer is interposed in a wave guide that is filled with solid dielectric material it can be supfported by a surrounding tube of that same material. In

ducers of Figs. 2 and 3, for example, generate the TEos mode in some slight degree, because the dielectric fills one ofthe like-phased cophasal zones of this mode (Fig. lC), and thus tends to generate the TEoa mode but it does not V.extend quite the proper distance into the adjacent oppositely-phased zone to effect cancellation. A secondary mode so generated will be suppressed, however, if its cutoff frequency is greater than the operating frequency, i. e.,

` If not so suppressed it may happen to be of such amplitude and phase as kto oppose and reduce a wave component of the same mode originating elsewhere in the guide. The generation lof any particular secondary mode can be obviated, in any event, by so disposing the dielectric material of the mode transducer that any dielectric material in one cophasal zone of that mode is balanced by dielectric material in a cophasal zone of the opposite phase. Applying this principle to the transducers of Figs. 2 and 3, for example,

it will be found that if the indicated radius is changed from 0.546a to 0.529a none of the TEua mode will be generated. l

Still another factor is the relation between the dielectric constants of the several dielectric media, that is, the two dielectric media in the transducer section and the dielectric medium in the adjoining sections of guide. The

more closely the average or effective dielectric constant in the transducer section approximates the dielectric constant in the adjoining sections, the more completely is the transducer reflectionless. The more nearly alike the dielectric constants of the media in the transducer section the lower are internal reflections and reflection losses in composite transducers such as the one illustrated in Fig. 6. The greater, too, is the length of transducer required, and in some cases this in itself is advantageous. lt will be understood, then, that as a special case the adjoining guide may contain a solid dielectric medium and the transducer may comprise a first dielectric of the same or lower dielectric constant and a second dielectric (a gas,

`for example) of still lower dielectric constant.

`particular problem in practice, the inventionisespecially well adapted to an empirical method of design-andfabrication. rllhis approach will b2 treated first andapplied to a specific example of practice before the more .general and elaborate mathematical approach is considered.

Assume for specific examplethat a transducer of the form shown in Fig. 3 is called upon to generate TEuz waves of predetermined amplitude and phase in a guide carrying pure TEo1 waves. Since .-the;amplitude of the generated TEoz waves depends on thelength of the dielectric member the latter can be fabricated in the form of washers which are assembled in the guide one after -another until the generated T E02 wa-ve is-increased to the desired amplitude. Then the dielectric assemblage is shifted longitudinally in the guide to a lposition such that the generated waves have the desired ,phase at the pre- -scribed point. This method of fabrication by parts is applicable also to other forms of dielectric transducer although the mechanical problem is greater in some cases than in others.

In carrying out the foregoing procedure a point may'be reached where additional washers contribute progressively less to the amplitude of the generated waves and, in fact, a point may be reached at which additionalwashers reduce the amplitude. If a greaterramplitude be required in such case additional Washers may be assembled in the same manner to form another dielectric tube at a distance along the guide where tests show they increase the amplitude further. lAlternatively in suchcase the first transducer element'may be followed directly'by one of the complementary form shown in Fig. 2. Mode transducer members conforming with Fig. 4 and/or Fig. 5 may be provided additionally if the TEos mode is to be generated at thesame time.

Where two or more dielectric transducer members appropriate to the same secondary mode are arranged in tandem for one reason or another,.the amplitude of the resultant generated wave -ean be adjusted precisely '-.by adjusting the distance between members, for this distance determines the relative phase in which the contribution from each member to the desired secondary modefcombines with the contributions from Vthe other members. The assemblage of dielectric -members may Vthen Pbe shifted, as a unit, to adjust the phase of the resultant generated wave as desired. The contributions from transducer members of the same form are directly additive if, in the interval between members, the fnumber of wavelengths cf the operating mode diers by an'integer A(e. '-g., l, 2, 3 from the number of wavelengths of the secondary mode being generated.

There is'little tendencyfo-r any of the generatedsecondary modes to give rise in any signicantdegreeto still other modes -by interaction ywith thevdielectric transducers, for the secondary modes will ordinarily be many times smaller in amplitude thanthe operating mode.

Fig. 6 illustrates a composite modeitransducer that is disposed adjacent the larger end of a conical waveguide adapter, or tapersection, 161m a TEM system andthat is designed to-substantially'neutralize TEuz and TEo3modes generated by the adapter. The dielectricV struct-ure may be divided into parts, as shown, for ease of manufacture. The lefthand dielectricelement maybe resolved into a cylindrical plug '18 and a TEoi-TEog'transducer 15 conforming with Fig. 5, the plugserving to x accurately the distance from the conical adapter to the transducer. This isvfollowed by another spacing plug 19, a TEoi-TEoz transducer 12 conforming with Fig. 3, and an element comprising another spacer 20 and a secondTEoi-Tloz transducer 11 complementary to the first.

In one instance in practice the conical adapter 1i6 .was twelve inches long andjoined twoair-iilled metal guides having inside diameters of two inches and 4.732 inches, respectively. The smaller` guide 17 wasgsupplied Vwith pure TEM waves i having aV free-space 4wavelength of 3.133

iirst approximation by a perturbation method.

centimeters. .The dielectric structure was con-structedof polystyrene foam having -a relative dielectric constant of 1.02.35 and a low power factor. The lengths `of `the spacers were 2.92, 4.19 and 5;6 4 centimeters, respectively, taking them in order frorndeft to rightfas they appear in Fig. 6. In the same order, the lengths of the transducer sections were 1.10, 5.07 and V5.07 centimeters, respectively, and the radii were scaled -as in Figs. 2 3 and 5 for maximum generation of -the two ksecondary modes. (Fig. 6shows the structure substantially to scale except for shortening of the adapter 16.)

It will be noted that the operation ofthe dielectric mode transducer does not depend on power absorption. The transducer tends instead to restore-.thepower receivedin the form of'spurious modes into the original mode. Although the function ofthe dielectric transducer in Fig. 6 is analogous to that of an optical lens 'in so far as it tends to restore the curved wavefront incident rupon it to planar form, :the principles of operation are distinctly different. Since the space dimensions involved are comparable with the wave length, geometric optics cannot be applied.

'homogeneous dielectric but containingno chargeandcurrent distributions in its interior, may be regarded as a superposition of y one or :more of the :transmission .modes characteristic of the cross-sectional .shape (round, rectangular, or other) of that particular guide. If an obstacle of different dielectric constant is now introduced into the guide, the amplitudes of these modes and in general the number of modes present .will be altered, .in lorder'that the total-fields may satisfyappropriateboundary conditions at the surface ofthe obstacle. .An-exact calculation ofthe amplitudes andlphasesof all the modes inducedby the presence ofthe-obstacle wouldfbean eX- ceedingly difficult undertaking in vany Vbut -the simplest special cases; but-it happens that if the-relative dielectric constant -of the obstacle differs only slightly from unity, we can calculate lits effecton the-wave guide elds to This method lwe now proceed tovdescribe.

It is shown in works on electromagneticitheory-(S. yA. Schelkunoif, lElectromagnetic Waves 'D. van Nostrand Co., Inc., New York, V1943,pp. 90-94) that ifa homogeneous dielectric island is placed in a harmonically varying electromagnetic field in anotherI dielectric medium, the

-etfcct of the islandon the eld may becalculated by replacing it with fictitious polarization currents and charges. If t-herelativefdielectric'constanterof the island differs but little -from unity, i. e.,if

(er-l) 1, er=e/eo (l) where e is the dielectric constantof theobstacle .and e0 the dielectric constant of the surrounding material, then we may obtain a first approximation to the effect` ofthe .dielectric onthe fields by assuming the polarization cur- 1 rents I and charges qsto be given by where Eo isthe electric eldwhichwould haveiexisted at `the point in question in the ,absenceofthe obstacle,'Eon is Electricity, 2nd ed., McGraw-Hill, INew York, 1950, pp.

l521623, 551, 552), one has only to integrate these expressions, suitably weighted, over the entire volume occupied by the dielectric in order to get the irst approximation to tbe change in the original field due to the presence of the dielectric. Presumably this {irst approximation might be used in turn to calculate a second approximation, and so forth.

Consider specifically, by way of example, the circular electric (TEum) modes characteristic of a round wave guide. There are an infinite number of these modes, of which however at most a finite number will propagate freely in a pipe of given diameter at a particular operating frequency. lf we take a cylindrical coordinate system (p, sv, z), where p=rz represents the inner surface of the guide and z is measured along the guide axis, the electric vector of these modes has only a :fa-component, which is independent of the angle p. The electric field of the TEom mode is given, up to an arbitrary amplitude factor by (S. A. Schelkunoif, Electromagnetic Waves, pp, S80-381, 389-390) :FF s (Em)w=J1(X0n-1P)e om, 711:1, 2, (4:)

where F0m=(X0m2-2)x =27rp` Here )t is the wavelength, at the operating frequency, of a free wave in an unbounded medium of dielectric constant en, and Xoma=kom is the mth positive root of the Bessel function 110:) :0. For the modes which are above cut-off (i. e., freely propagated) at the operating frequency we may write where )tom is the wavelength of the TEnm wave in the guide. The field pattern of the circular electric modes in any plane normal to the axis of the guide is quite simple, the electric lines of force being merely concentric circles. The electric field vanishes on the axis of the guide and at the perfectly conducting outer wall; in addition there are, for the TEom mode, (m-l) nulls of electric field between the axis and the guide wall.

If in a round wave guide the electric ield vector has only a go-component, the field may always be regarded as a super-position of one or more TEom modes with appropriate amplitudes and phases. lf the wave guide extends indenitely, in the positive z-direction and there is no generation, reflection, or absorption of modes to the right of some reference plane z=zo, then for zzo we may write EFZlAmJltXtmne rom' 7) where the Ams are complex constants (of which all but a finite number may be zero). We shall call Am the amplitude of the TEom component of the field whose electric vector is given by (7). The choice of how we define unit amplitude of a given mode is of course arbitrary, the definition adopted here being simplest for our present purpose.

Suppose that We have a wave guide propagating an ,initially pure TEoi wave in the positive z-direction, the

electric eld of this wave being given by E..=AJ. Xmp)e Tm (s) If we insert a rotationally symmetric dielectric obstacle coaxially into the guide then, unless the dielectric forms a solid cylinder completely filling a section of guide between two transverse planes, in addition to altering the amount of TEoi mode present it will generate TEoz, TEos, modes in amounts depending on the dimensions and shape of the obstacle. The total electric field in the guide may then be written as E =Eo p-l-(er-1)Ei p (9) where (er-DEW is the eld induced by the presence of the obstacle of relative dielectric constant er. I The factor (er-l) is inserted explicitly since if er differs but slightly from unity the quantity Bnp can be calculated as a function of the geometry of the obstacle, the radius of the guide, and the operating wavelength, independent of er to first approximation. A

To the right of the obstacle we evidently have where (er-DB1 is the relative amplitude of the TEnm mode generated by the interaction between the dielectric and the original TEor eld. If (er-1) 1, the Bms may be calculated as described above, by replacing the dielectric by elementary rings of polarization current with current density given by (2) and (8). Since the electric field is tangential to the surface of the obstacle there will be no surface polarization charges.

Calculation shows that the relative amplitudes of TE02 and TEna waves generated by the dielectric structures of Figs. 2 to 5, dirnensioned for maximum mode genera-tion as described, are as follows:

Here Bz and B3 have the meaning as in Equation 10, and as before Inspection of Equations l1-l6 shows that on account of the sine factors the Bms do not increase in magnitude indefinitely as l is increased but are oscillatory functions of the lengths of the dielectric cylinders. (This is in contrast to the predictions of a too naive wavefront argument, which might lead one to imagine that the distortion of the wavefront could be increased indefinitely by slowing down certain portions of the wavefront with a dielectric cylinder of arbitrarily great length.)

Suppose then that in a wave guide (say for zzo, where zo is some reference plane) the electric field is given by The field represented by (18) consists predominantly of the TEoi mode, with small amounts of TEoz, TEoa, etc.,

present' as impurities. IWe assumefthat the -mo'desabove -by calculation or by experimental measurement. Then Iwith the help of Equations Al1-1l6 we candetermine proper dirnensionsand spacing for an array of hollow dielectric cylinders Whose interactions withthe TEol -cornpo- -nentofthe original eld (1l-8) `will-generatelhigher mode fields ofA amplitude and phase just suirlcientto'ca-ncelout the -TEoz and TE03modes occurringlin (18). `Compar- -ing (9) and(10) with (18) we see'that the Vconditions to be met are (ef-1v) 232:-@2

Where the summation signs .merely indicate that'we .are

lto iadd the contributions `from all-the elementary .cylinders of which the lens will be made. If (20) and (21) Vare .satisfied simultaneously, then at any vpoint beyond the lens weeshouldfind only the TE01mode plus modes which are beyond cut-off atthegiven frequency. The

latter `modes represent localelds .which vanish withiml a few `wavelengths from the obstacle, leaving a pure TEM wave.

In applying the invention to the-compensationrof a conical adapter, as in Fig. 6, some .assistancefrnay be derived from the following approximate theoretical formulate expressing therelative amplitude and phase of certain lmodesgenerated in Y such an adapter.

The field in the guide at the larger end of the conical section is given approximately by sired choices of m and a. The values of C201) and C3( x),/for a ranging from 0.0to 1.2, are given inthe 'following table:

Since the Expression 22 for the fields in theV guide which follows the tapered section is of exactly the same form as (18), with known values of the coefficients Cm, We can applyfthe precedingptheory to design a transducer which will eliminate the undesired higher modes appearing i-n it.

fAs a numerical example consider-astructure to-cornpensatefor `a tapered section l2 inches long, which-joins aguidev-of inside diameter 12 inches toa guide kof inside diameter 4.732 inches. At the design wavelength .of .-3.33 .centimeters the only.,circularielectric mode which 10 '-.willpropagate Ain the `small vguide is `!1l:`.o1,.Whileithe Ilarge s'guidewill supportT-Eor, 11111302, fand :'Eoa. Wetset l1:16.01 Acm. \=3.3'3I cm.

L=52.79 cm.

where L lis the perpendicular distance gfrom the -vertex of the -conical section tothe -mouth `:of the lang-e guide The guide wavelengths of the propagatingcirc-:ularelectric modes are:

o1=3.54 Cm., )\02=4.24 cm., .03=7.54 Cm. (25) For the relative dielectric constant of the'transducer material we shall take er=ll0235 (26) this .being the value measured for -a-particular sample of polystyrene foam, with an uncertainty of perhaps vtwo y.orthree units in the lastfigure.

The first step in designing the transducer is to obtain the coeflcientsCz andfCa forthe `particular taper=em .-ployed. Wefindfrom (23),.(24),-and(=25;) that then by interpolation in the foregoing table,

C2=0.1472ef1-557 (28) =.Ca=0.399ei1-858 #(29) To eliminate the TEoz and TEos Vrnode elds in the region beyond thetransducer we must satisfy (20) .and (21). We shall satisfy these conditions by successive approximations. Since according to (28) and (29) the TEoz mode predominates over ,TEosfin-.the originaleld, we first design a cylinder which eliminates'TEoz, i.`e., which satisfies (20) without regard to (21). We then design, using (21), a second cylinder to compensate for the total TEo3 amplitude generated by the tapered section plus the first cylinder. *Since the amount of TEoz mode reintroduced by the second cylinderfis negligible,-the.trans ducer is then complete.

'In order to satisfy (20) we take a'ho'llow cylinder of the form shown in Fig. 3 whose internal and external .radii are `0.5.4,6a---328 centimeters and .4:26:01 .centimeters, and whose length and position are to bedetermined. .Substitutingfor B2.from (11.3.), fore, from.(.26),

and for C2-from (28), we find that (20) .becomes 0.1086 sin 0'5821 e #wwwa/a: Olimpia flnasmuchaas Athe absolute vvaluefoft-he `sine factorgoa-nnot fexceedunity, wesee lthatwitha transducerfofisuchrlow dielectric constant itV is :necessary `.to-correct the fTEnz Amode with two cylinders,;the .secondI one being'thecornplement .ofgthefrst and-fbeingplace'd at such apointzinfthe :guide that beyond the transducerfthe contributions-of Athetwo -cylinders add inf'phase. `lEf wegrequirethe firstcylinder ltolcancelfhalf ofthe total TEoz'eld, vweget On equating the moduli ofthe. complex members on both Vsides of (31),.weget .The complementaryi cylinder :which `cancelstfhe other; half :of :the zTEoz eldhaswthe-form of Pig. 2,swith=a Vradius of 1l 3.28 centimeters and a length of 5.07 centimeters. Its distance c from the mouth of the guide is determined by Next we have to calculate the total amplitude of TEos mode introduced by the tapered section plus the two cylinders already designed. Let this amplitude be Cs", then from (29), (14) and (12),

To cancel this TEos iield we introduce the pair of coaxial cylinders shown in Fig. 5, the radii of the inner cylinder being and 0.377a=2.26 cm. (36) while the radii of the outer cylinder are 0.690a=4.l4 cm. and a=6.0l cm. (37) The length l" and position c" of these cylinders are determined by (ef-1) B3=Cs (38) which becomes, if we refer to (16) and substitute numerical values,

c"=2.92 cm.

An axial section of the complete transducer is shown in Fig. 6.

Referring now to Fig. 7, there is illustrated an embodiment of the present invention in which a dielectric mode transducer is incorporated in a microwave device that tends to generate a spurious mode. The particular device shown is a 90-degree arcuate bend 23 in a round wave guide in which the energy is supplied in the TEoi mode. The theory of propagation of TEoi waves around a curved bend has been extensively treated in the literature (see for example M. louguet, Cables et Transmission l, 133- 153 (1947)), and it is there shown that when such a bend is encountered the applied TEoi waves are progressively converted into the TMn mode` I t is also known that the two modes have exactly the same phase velocity in a straight pipe, a circumstance which leads to close coupling between these two modes in a curved guide. In the bend the conversion into the TMu mode may be partial or complete, depending on the dimensions, and in fact there may be several complete conversions from one mode to the other in alternation.

In Fig. 7 the dielectric member 22 isA disposed uniformly throughout the arcuate length of the bend 23, `in accordance with the design principles set forth hereinbefore, to generate from the operating mode the same mode that the bend itself tends to generate, viz., the TMii mode. More particularly, the member 22 is proportioned to generate this mode with the same amplitude as that generated by the bend and with the same orientation. The relative phases are opposite so that the spurious mode generated in the bend is cancelled as rapidly as it is formed. In general the centroid of the dielectric-lled area is displaced somewhat from the geometrical center of the guide cross section toward the center of curvature vof the bend. The optimum position of the dielectric and the necessary cross-sectional area can be calculated fairly readily since the literature teaches what amount of the TMii mode must be 'cancelled per unit length of curved guide.V In the specific example lillustrated in Fig. 7 the dielectric member appears in cross section as a ISO-degree segment the chord of which is perpendicular` tothe plane of the bend. In a relatively sharp bend it may be necessary to use material having a dielectric constant substantially higher than the values hereinbefore suggested if there is to be complete cancellation of all of the TMn mode. In any such :case the extremities of the dielectric member may be tapered to reduce the tendency toward impedance mismatch.

The detailed design of the dielectric member 22 in Fig. 7 may be arrived at empirically. If, for example, the ISO-degree segment shown in Fig. 7 is found to overcompensate the bend, it may be removed and material shaved from its flat face until test shows that the emerging wave is substantially free of the TMn mode. Alternatively the dielectric member may be in the form of a flexible strip which can be progressively reduced in width until the desired condition is obtained. The member may be cemented in place, or supporting plugs may be used at its extremities, or other devices for holding it in position may be employed as will be evident to those skilled in the art. The subject matter of Fig. 7 is further disclosed and claimed in my application Serial No. 530,914, filed April 26, 1956.

The technique described with reference to Fig. 7 can be applied also to other operating modes and cross sections such as, for example, the dominant mode in an oversized, rectangular guide, the dielectric member being disposed with reference to the cophasal zones involved in accordance with the principles set forth hereinbefore. It will be understood, too, that the mode transducer may alternatively precede and/or follow the bend, in which case the spurious mode appears in the bend although not in the output section of guide.

Another practical application of the dielectric mode transducer is illustrated in Fig. 8. Here a wave source 25 delivers power in the dominant mode TEio to a rectangular guide 26 which leads to a mode converter 27. The latter more or less completely transforms the wave power into the TEM mode in a circular guide 1 0 for transmission therethrough. The converter Z7 tends to produce also spurious modes and these are cancelled by the mode transducer 28 which follows it. OneV form of converter, for example, comprises a hollow-pipe guide the cross section of which is deformed progressively along its length from rectangular shape into the sector of a circle supporting the TEm sectoral mode, the sector progressively Haring out in turn until the angle reaches 360 degrees and `the sectoral mode converted into the TEni circular electric mode. Another form of converter involves the simultaneous expansion of two sectors, each of which carries half of the nal circular electric mode and operates to convert the TEzn mode in a rectangular guide into the TEM mode in a round guide. Such transducers, unless made very long compared to the transverse dimensions of the Wave guides, introduce spurious modes such as TE11 and TEzi into the TEoi output.

To cancel the TE11 mode the mode transducer 28 may comprise ,a section of round guide in which .dielectric material is disposed on one side only of a plane forming a diameter of the guide, as in Fig. 2A or Fig. 9A, for example. To cancel the TE21 mode the transducer may comprise also a section in which dielectric material is disposed symmetrically in opposite quadrants, for ex,- ample as illustratedin Fig. 8A, the rotational position of the dielectric being adjusted, of course, inaccordance with the particular orientation of the TEzi mode to be cancelled. y l

In the embodiment of-A the invention illustrated in Vtion relative'to theplane of the bend.

13 Fig. 9 advantage Ais taken of the "fact that the TEoi and TMn modes in a round guide have the 'same phase velocity, to make the longitudinalposition o f the dielectric mode transducer uncritical and to secure otheradvantages as will presentlyappear.

A curved wave guide has several natural modes, that is,.modes which it will propagate ,without mode conversion. Two of these natural modes ina curved guide of circular cross section are known as the TE01-l-.TM11" and TE01-TM11, each comprising a TEoi component and an equal T-Mn component .with a particular orienta- In Fig. 9 a dielectric rnode transducer 30'immediate1y preceding the bend 23 converts half the;power Vof the'incoming TEot waves into the TMn mode oriented to conform with one'oftthese two naturalmojdesoftheabend. The total wave power'proceeds to and through thefbend .without further mode conversion to -azsecond dielectrictransducer 31, identical withfthe first, which transforms ,the wave power back into the TEoi mode. Y

The cross section of the ldielectric members in Fig. 9 is inthe form of a sector `of 'half-angle a disposed with the -bisector in the ,plane of the bend. If the 'TEoi-t-TMn mode be chosen, the dielectric is disposed towardthe outside of the bend, that'ispwith thebisector directed away from thecenter of curvature of the bend.

The length land the half-.angle Yorofeach transducer mayv be calculated as follows:

Thehalf-angle ais afunction only ofthe ratio v -:M M, where A is the free wavelength corresponding tothe `operating frequencyand \=21ra/ 3.83.17 isthe cut-off .wavelength for the TEoi and T-Mn modesiina straightg-uide of the given radiusa. in radians satisfies the equation where a 1r. This equation may be solved readily by cut and try for any particular value of u.

When a has been determined, the required length l of each mode transducer is given by 0.6823( e,.-1) sin a where er is the relative dielectric constant of the transducer material, and it is assumed that er does not differ much from unity.

If, for specific example, is 1.875 centimeters and a is 1.27 centimeters, 1 is calculated to be 0.90 and a, derived from (42), is 40.4 degrees. If er is 1.0200, (43) indicates a length l of about 212 centimeters. Increasing er to 1.0235 reduces l to about 180 centimeters.

Since the phase velocities of the TEoi and TMn modes are identical in a straight guide it is evident that it makes no difference whether or not there is any separation between the ends of the transducers and the ends of the curved section in Fig. 9. Also the transducers may be made in several separated parts if desired so long as the total length of the various parts is equal to the required value of l. The dielectric members may be supported in the guide if necessary by solid dielectric plugs at both ends. The transducer described does not tend to generate modes other than TMn in any substantial degree since all modes other than TMn differ in phase velocity from the TEoi mode. Hence over a distance of many wavelengths tnese other modes will phase in and out so often that the net power transfer will be small.

A .third natural mode of the bend is the TM11 mode, which has a different orientation from the TMu" mode, but has the same velocity as the TEoi mode in a straight guide. The TMn mode could be produced from TEoi, if desired al-ternatively, by a transducer designed according to the general principles described above, and transmitted around the bend inthe same way as TEoiizTMn".

Cos a= (42) Numerous other embodiments within the spirit and scopeo'fthe invention, in a'dditionto those .specifically described'herein, will'be obvious tothoseskilled inthe art.

What is claimed is:

A1. In combination, a closed conductive-walled wave guide of circular crosssection comprising `a flaring sectionjoined at its larger end to a section of uniform size, and a mode transducer in said uniform seotionadjacent said flaring section, said transducer comprising a general- ,ized cylinder of dielectric material substantially confined to oneof the cophasal regions of a circular electric TEon modeof electromagnetic wave propagation, where ln is "greater than one.

2. lIn combination, a closed conductive-walled wave .gui'de'of substantially circular cross section comprising va'flaring section Vjoined at one end to a :section of `-uni- Iform size, and a mode transducer in saidiuniform section comprising a generalized cylinder of ydielectric material substanti-ally confined to oneof the cophasal regions-of a circular electric TEO mode of electromagnetic wave'propagation, where n is greater thanone.

3. In combination, `a hollow circular multiple mode wave -guidehaving a straight section and a transitionsec- `tion and'having ,conducting lside walls, said wave guide `being substantially filled with .a medium having a ngiven ,dielectric constant, `rneans'for applying microwave energy to saidy wave guide inthe TEoi electromagnetic wave mode .at a frequency sufficiently high that at least four additional imodes may Ibe readily propagated `through said wave guide, said straight length of 'said wave lguide-'having .a predetermined axis, means comprising said transition sectionot said wave guide "for converting 2L-portion yof the microwave energy Vapplied to said waveguide from vsa'idFEoi mode intoa second one of s aid m-odes'having a given'amplitude and phase at one point in-said vwave guide, .said transition section being coupled -tov said-straight section of wave guide and having conducting walls which progressively vary in their spacing from said predetermined axis, said second mode having first electric field regions which are oppositely phased with respect to the electric field of said TEoi mode and having second electric field regions having the same phase as the electric field of said TEM mode which exists in the same regions, and means comprising a dielectric mode transducer in said wave guide and extending across only a portion of the crosssection of said guide for converting an additional portion of said TEoi Inode into wave energy in said second mode, said transducer having such a length that the amplitude of said second mode produced thereby is equal to said given amplitude of said second mode produced by said transition section, said mode transducer being so spaced from said transition section that the phase of the second mode produced by said transducer is opposite to that produced by said transition section at said one point, said mode transducer also being located predominantly in only one of said first and second regions, and the dielectric constant of said transducer differing from that of said medium by not more than approximately tten per cent.

4. In combination, a hollow circular multiple mode wave guide having a straight section and a transition section and having conducting side walls, means for applying microwave energy to said wave guide in the TEoi electromagnetic wave mode at a frequency sufficiently high that at least four additional modes may be readily propagated through said wave guide, said straight length of said wave guide having a predetermined axis, means comprising said transition section of said wave guide for converting a portion of `the microwave energy applied to said wave guide from said TEoi mode into a second one of said modes having a given amplitude and phase at one point in said wave guide, said transition section being coupled to said straight section of wave guide and having conducting walls which progressively vary in their spacing from said predetermined axis, said second mode having first electric iield regions which are oppositely phased with respect to the electric iield of said TEui mode and having second electric field regions having the same phase as the electric field of said TEoi mode which exists in the same regions, and means comprising a dielectric mode transducer in said wave guide and extending across only a portion of the cross-section of said guide -for converting an additional portion of said TEoi mode into 4wave energy in said second mode, said `transducer having such a length that the amplitude of said second mode produced thereby is equal to said given amplitude of said second mode produced by said transition section, said mode transducer being so spaced from said transition section that the phase of the second mode produced by said transducer is opposite to that produced by said transition section at said one point, and said mode transducer being located predominantly in only one of said rst and second regions.

5. A combination as `deiined in claim 4 wherein said transition section is a bend.

6. A combination as defined in claim 4 wherein said transition section is a taper.

7. In combination, a hollow circular multiple mode wave guide having a straight section and a transition section and having conducting side walls, means -for applying microwave energy to said wave guide in a preassigned electromagnetic wave mode at a frequency sufliciently high that several additional modes may -be readily propagated through said Wave guide, said straight length of said wave guide having a predetermined axis, means comprising said transition section of said Wave guide for converting a portion ofy the microwave energy applied to said wave guide from said preassigned mode into a second one of said modes having a given amplitude and phase at one point in said Wave guide, said transition section being coupled to said straight section of wave guide and having conducting walls which progressively vary in their spacing from said predetermined axis, said second mode having iirst electric field regions which are oppositely phased with respect to the electric field of said preassigned Inode and having second electric field regions having the same phase as the electric field of said preassigned mode which exists in the same regions, and means comprising a dielectric mode transducer in said wave ,'guide' and extending across only a portion of the crosssection of said guide for converting an additional portion of said preassigned mode into wave energy in said second mode, said transducer having such a length that the arnplitude of said second mode produced thereby is equal to said given amplitude of said second mode produced by said transition section, said mode transducer being so spaced from said transition section that the phase of the second mode produced by said transducer is opposite to that produced by said transition section at said one point, and said -mode transducer being located predominantly in only one of said rst and second regions.

References Cited in the iile of this patent UNITED STATES PATENTS 2,129,712 Southworth sept. 13,1938 2,411,534 Fox Nov. 26, 1946 2,425,345 Ring Aug. 12, 1947 2,433,368 Johnson Dec. 30, 1947 2,438,119 Fox Mar. 23, 1948 2,511,610 Wheeler June 13, 1950 2,540,839 Southworth Feb. 6, 1951 2,599,753 FOX June 10, 1952 2,611,087 Alford Sept. 16, 1952 2,632,806 Preston Mar. 24, 1953 2,656,513 King Oct. 20, 1953 FOREIGN PATENTS Great Britain Ian. 2l, 1948 

